St000425The number of occurrences of the pattern 132 or of the pattern 213 in a permutation. St000426The number of occurrences of the pattern 132 or of the pattern 312 in a permutation. St000428The number of occurrences of the pattern 123 or of the pattern 213 in a permutation. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000437The number of occurrences of the pattern 312 or of the pattern 321 in a permutation. St000456The monochromatic index of a connected graph. St000592The number of occurrences of the pattern {{1},{2},{3}} such that 1 is maximal. St001541The Gini index of an integer partition. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St000224The sorting index of a permutation. St000797The stat`` of a permutation. St001080The minimal length of a factorization of a permutation using the transposition (12) and the cycle (1,. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001930The weak major index of a binary word. St000108The number of partitions contained in the given partition. St000033The number of permutations greater than or equal to the given permutation in (strong) Bruhat order. St000545The number of parabolic double cosets with minimal element being the given permutation. St000880The number of connected components of long braid edges in the graph of braid moves of a permutation. St001684The reduced word complexity of a permutation. St000881The number of short braid edges in the graph of braid moves of a permutation. St001856The number of edges in the reduced word graph of a permutation. St000226The convexity of a permutation. St000879The number of long braid edges in the graph of braid moves of a permutation. St000958The number of Bruhat factorizations of a permutation. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001855The number of signed permutations less than or equal to a signed permutation in left weak order. St000957The number of Bruhat lower covers of a permutation. St000458The number of permutations obtained by switching adjacencies or successions. St001003The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001254The vector space dimension of the first extension-group between A/soc(A) and J when A is the corresponding Nakayama algebra with Jacobson radical J. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001769The reflection length of a signed permutation. St001822The number of alignments of a signed permutation. St001864The number of excedances of a signed permutation. St001866The nesting alignments of a signed permutation. St001905The number of preferred parking spots in a parking function less than the index of the car. St001171The vector space dimension of $Ext_A^1(I_o,A)$ when $I_o$ is the tilting module corresponding to the permutation $o$ in the Auslander algebra $A$ of $K[x]/(x^n)$. St001805The maximal overlap of a cylindrical tableau associated with a semistandard tableau. St001861The number of Bruhat lower covers of a permutation. St001896The number of right descents of a signed permutations. St001946The number of descents in a parking function. St000135The number of lucky cars of the parking function. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001927Sparre Andersen's number of positives of a signed permutation. St000136The dinv of a parking function. St000194The number of primary dinversion pairs of a labelled dyck path corresponding to a parking function. St000359The number of occurrences of the pattern 23-1. St000365The number of double ascents of a permutation. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000441The number of successions of a permutation. St000632The jump number of the poset. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000832The number of permutations obtained by reversing blocks of three consecutive numbers. St000848The balance constant multiplied with the number of linear extensions of a poset. St000849The number of 1/3-balanced pairs in a poset. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001114The number of odd descents of a permutation. St001152The number of pairs with even minimum in a perfect matching. St001405The number of bonds in a permutation. St001413Half the length of the longest even length palindromic prefix of a binary word. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001520The number of strict 3-descents. St001532The leading coefficient of the Poincare polynomial of the poset cone. St001556The number of inversions of the third entry of a permutation. St001565The number of arithmetic progressions of length 2 in a permutation. St001596The number of two-by-two squares inside a skew partition. St001633The number of simple modules with projective dimension two in the incidence algebra of the poset. St001644The dimension of a graph. St001712The number of natural descents of a standard Young tableau. St001768The number of reduced words of a signed permutation. St001772The number of occurrences of the signed pattern 12 in a signed permutation. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001778The largest greatest common divisor of an element and its image in a permutation. St001820The size of the image of the pop stack sorting operator. St001821The sorting index of a signed permutation. St001823The Stasinski-Voll length of a signed permutation. St001860The number of factors of the Stanley symmetric function associated with a signed permutation. St001862The number of crossings of a signed permutation. St001863The number of weak excedances of a signed permutation. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St001894The depth of a signed permutation. St001903The number of fixed points of a parking function. St001935The number of ascents in a parking function. St001937The size of the center of a parking function. St001942The number of loops of the quiver corresponding to the reduced incidence algebra of a poset. St001948The number of augmented double ascents of a permutation. St000039The number of crossings of a permutation. St000064The number of one-box pattern of a permutation. St000080The rank of the poset. St000222The number of alignments in the permutation. St000236The number of cyclical small weak excedances. St000237The number of small exceedances. St000239The number of small weak excedances. St000241The number of cyclical small excedances. St000245The number of ascents of a permutation. St000355The number of occurrences of the pattern 21-3. St000431The number of occurrences of the pattern 213 or of the pattern 321 in a permutation. St000433The number of occurrences of the pattern 132 or of the pattern 321 in a permutation. St000516The number of stretching pairs of a permutation. St000696The number of cycles in the breakpoint graph of a permutation. St000731The number of double exceedences of a permutation. St000799The number of occurrences of the vincular pattern |213 in a permutation. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000837The number of ascents of distance 2 of a permutation. St000845The maximal number of elements covered by an element in a poset. St000846The maximal number of elements covering an element of a poset. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000888The maximal sum of entries on a diagonal of an alternating sign matrix. St000892The maximal number of nonzero entries on a diagonal of an alternating sign matrix. St000898The number of maximal entries in the last diagonal of the monotone triangle. St000910The number of maximal chains of minimal length in a poset. St000942The number of critical left to right maxima of the parking functions. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001010Number of indecomposable injective modules with projective dimension g-1 when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001082The number of boxed occurrences of 123 in a permutation. St001095The number of non-isomorphic posets with precisely one further covering relation. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001130The number of two successive successions in a permutation. St001200The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001209The pmaj statistic of a parking function. St001210Gives the maximal vector space dimension of the first Ext-group between an indecomposable module X and the regular module A, when A is the Nakayama algebra corresponding to the Dyck path. St001231The number of simple modules that are non-projective and non-injective with the property that they have projective dimension equal to one and that also the Auslander-Reiten translates of the module and the inverse Auslander-Reiten translate of the module have the same projective dimension. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001234The number of indecomposable three dimensional modules with projective dimension one. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St001298The number of repeated entries in the Lehmer code of a permutation. St001330The hat guessing number of a graph. St001332The number of steps on the non-negative side of the walk associated with the permutation. St001396Number of triples of incomparable elements in a finite poset. St001423The number of distinct cubes in a binary word. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001510The number of self-evacuating linear extensions of a finite poset. St001516The number of cyclic bonds of a permutation. St001535The number of cyclic alignments of a permutation. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001557The number of inversions of the second entry of a permutation. St001594The number of indecomposable projective modules in the Nakayama algebra corresponding to the Dyck path such that the UC-condition is satisfied. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St001745The number of occurrences of the arrow pattern 13 with an arrow from 1 to 2 in a permutation. St001771The number of occurrences of the signed pattern 1-2 in a signed permutation. St001811The Castelnuovo-Mumford regularity of a permutation. St001817The number of flag weak exceedances of a signed permutation. St001845The number of join irreducibles minus the rank of a lattice. St001846The number of elements which do not have a complement in the lattice. St001851The number of Hecke atoms of a signed permutation. St001857The number of edges in the reduced word graph of a signed permutation. St001867The number of alignments of type EN of a signed permutation. St001868The number of alignments of type NE of a signed permutation. St001870The number of positive entries followed by a negative entry in a signed permutation. St001873For a Nakayama algebra corresponding to a Dyck path, we define the matrix C with entries the Hom-spaces between $e_i J$ and $e_j J$ (the radical of the indecomposable projective modules). St001892The flag excedance statistic of a signed permutation. St001893The flag descent of a signed permutation. St001895The oddness of a signed permutation. St001902The number of potential covers of a poset. St001904The length of the initial strictly increasing segment of a parking function. St001926Sparre Andersen's position of the maximum of a signed permutation. St001960The number of descents of a permutation minus one if its first entry is not one. St000001The number of reduced words for a permutation. St000028The number of stack-sorts needed to sort a permutation. St000062The length of the longest increasing subsequence of the permutation. St000133The "bounce" of a permutation. St000155The number of exceedances (also excedences) of a permutation. St000186The sum of the first row in a Gelfand-Tsetlin pattern. St000199The column of the unique '1' in the last row of the alternating sign matrix. St000213The number of weak exceedances (also weak excedences) of a permutation. St000255The number of reduced Kogan faces with the permutation as type. St000314The number of left-to-right-maxima of a permutation. St000335The difference of lower and upper interactions. St000446The disorder of a permutation. St000463The number of admissible inversions of a permutation. St000494The number of inversions of distance at most 3 of a permutation. St000519The largest length of a factor maximising the subword complexity. St000528The height of a poset. St000672The number of minimal elements in Bruhat order not less than the permutation. St000693The modular (standard) major index of a standard tableau. St000719The number of alignments in a perfect matching. St000744The length of the path to the largest entry in a standard Young tableau. St000882The number of connected components of short braid edges in the graph of braid moves of a permutation. St000896The number of zeros on the main diagonal of an alternating sign matrix. St000906The length of the shortest maximal chain in a poset. St000922The minimal number such that all substrings of this length are unique. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. St000945The number of matchings in the dihedral orbit of a perfect matching. St000956The maximal displacement of a permutation. St000996The number of exclusive left-to-right maxima of a permutation. St001090The number of pop-stack-sorts needed to sort a permutation. St001164Number of indecomposable injective modules whose socle has projective dimension at most g-1 (g the global dimension) minus the number of indecomposable projective-injective modules. St001227The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001245The cyclic maximal difference between two consecutive entries of a permutation. St001246The maximal difference between two consecutive entries of a permutation. St001288The number of primes obtained by multiplying preimage and image of a permutation and adding one. St001415The length of the longest palindromic prefix of a binary word. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001424The number of distinct squares in a binary word. St001433The flag major index of a signed permutation. St001485The modular major index of a binary word. St001555The order of a signed permutation. St001566The length of the longest arithmetic progression in a permutation. St001589The nesting number of a perfect matching. St001618The cardinality of the Frattini sublattice of a lattice. St001622The number of join-irreducible elements of a lattice. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St001697The shifted natural comajor index of a standard Young tableau. St001726The number of visible inversions of a permutation. St001770The number of facets of a certain subword complex associated with the signed permutation. St001812The biclique partition number of a graph. St001925The minimal number of zeros in a row of an alternating sign matrix. St000018The number of inversions of a permutation. St000019The cardinality of the support of a permutation. St000029The depth of a permutation. St000044The number of vertices of the unicellular map given by a perfect matching. St000060The greater neighbor of the maximum. St000144The pyramid weight of the Dyck path. St000197The number of entries equal to positive one in the alternating sign matrix. St000209Maximum difference of elements in cycles. St000210Minimum over maximum difference of elements in cycles. St000216The absolute length of a permutation. St000443The number of long tunnels of a Dyck path. St000643The size of the largest orbit of antichains under Panyushev complementation. St000653The last descent of a permutation. St000780The size of the orbit under rotation of a perfect matching. St000809The reduced reflection length of the permutation. St000863The length of the first row of the shifted shape of a permutation. St000890The number of nonzero entries in an alternating sign matrix. St000924The number of topologically connected components of a perfect matching. St000963The 2-shifted major index of a permutation. St000988The orbit size of a permutation under Foata's bijection. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the Dyck path. St001015Number of indecomposable injective modules with codominant dimension equal to one in the Nakayama algebra corresponding to the Dyck path. St001016Number of indecomposable injective modules with codominant dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001041The depth of the label 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001077The prefix exchange distance of a permutation. St001131The number of trivial trees on the path to label one in the decreasing labelled binary unordered tree associated with the perfect matching. St001180Number of indecomposable injective modules with projective dimension at most 1. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001226The number of integers i such that the radical of the i-th indecomposable projective module has vanishing first extension group with the Jacobson radical J in the corresponding Nakayama algebra. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001297The number of indecomposable non-injective projective modules minus the number of indecomposable non-injective projective modules that have reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001480The number of simple summands of the module J^2/J^3. St001497The position of the largest weak excedence of a permutation. St001511The minimal number of transpositions needed to sort a permutation in either direction. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St001782The order of rowmotion on the set of order ideals of a poset. St001806The upper middle entry of a permutation. St001854The size of the left Kazhdan-Lusztig cell, St001911A descent variant minus the number of inversions. St001958The degree of the polynomial interpolating the values of a permutation. St000004The major index of a permutation. St000030The sum of the descent differences of a permutations. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000339The maf index of a permutation. St000393The number of strictly increasing runs in a binary word. St000485The length of the longest cycle of a permutation. St000487The length of the shortest cycle of a permutation. St000501The size of the first part in the decomposition of a permutation. St000673The number of non-fixed points of a permutation. St000692Babson and Steingrímsson's statistic of a permutation. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000735The last entry on the main diagonal of a standard tableau. St000794The mak of a permutation. St000833The comajor index of a permutation. St000841The largest opener of a perfect matching. St000844The size of the largest block in the direct sum decomposition of a permutation. St001002Number of indecomposable modules with projective and injective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001040The depth of the decreasing labelled binary unordered tree associated with the perfect matching. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001117The game chromatic index of a graph. St001170Number of indecomposable injective modules whose socle has projective dimension at most g-1 when g denotes the global dimension in the corresponding Nakayama algebra. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001267The length of the Lyndon factorization of the binary word. St001289The vector space dimension of the n-fold tensor product of D(A), where n is maximal such that this n-fold tensor product is nonzero. St001519The pinnacle sum of a permutation. St000625The sum of the minimal distances to a greater element. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001019Sum of the projective dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001468The smallest fixpoint of a permutation. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St000825The sum of the major and the inverse major index of a permutation. St000111The sum of the descent tops (or Genocchi descents) of a permutation. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St001259The vector space dimension of the double dual of D(A) in the corresponding Nakayama algebra. St001858The number of covering elements of a signed permutation in absolute order. St001865The number of alignments of a signed permutation. St001613The binary logarithm of the size of the center of a lattice. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001881The number of factors of a lattice as a Cartesian product of lattices. St001615The number of join prime elements of a lattice. St001616The number of neutral elements in a lattice. St001617The dimension of the space of valuations of a lattice. St001623The number of doubly irreducible elements of a lattice. St001624The breadth of a lattice. St001625The Möbius invariant of a lattice. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001720The minimal length of a chain of small intervals in a lattice. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001621The number of atoms of a lattice. St001626The number of maximal proper sublattices of a lattice. St001877Number of indecomposable injective modules with projective dimension 2. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St001875The number of simple modules with projective dimension at most 1. St001681The number of inclusion-wise minimal subsets of a lattice, whose meet is the bottom element. St001619The number of non-isomorphic sublattices of a lattice. St001168The vector space dimension of the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001666The number of non-isomorphic subposets of a lattice which are lattices. St001833The number of linear intervals in a lattice. St001677The number of non-degenerate subsets of a lattice whose meet is the bottom element. St001620The number of sublattices of a lattice. St001679The number of subsets of a lattice whose meet is the bottom element. St000068The number of minimal elements in a poset. St000181The number of connected components of the Hasse diagram for the poset. St000454The largest eigenvalue of a graph if it is integral. St000782The indicator function of whether a given perfect matching is an L & P matching. St000908The length of the shortest maximal antichain in a poset. St000911The number of maximal antichains of maximal size in a poset. St000914The sum of the values of the Möbius function of a poset. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001208The number of connected components of the quiver of $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra $A$ of $K[x]/(x^n)$. St001414Half the length of the longest odd length palindromic prefix of a binary word. St001487The number of inner corners of a skew partition. St001490The number of connected components of a skew partition. St001635The trace of the square of the Coxeter matrix of the incidence algebra of a poset. St001722The number of minimal chains with small intervals between a binary word and the top element. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001884The number of borders of a binary word. St001890The maximum magnitude of the Möbius function of a poset. St000043The number of crossings plus two-nestings of a perfect matching. St000075The orbit size of a standard tableau under promotion. St000084The number of subtrees. St000100The number of linear extensions of a poset. St000168The number of internal nodes of an ordered tree. St000281The size of the preimage of the map 'to poset' from Binary trees to Posets. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St000295The length of the border of a binary word. St000298The order dimension or Dushnik-Miller dimension of a poset. St000307The number of rowmotion orbits of a poset. St000328The maximum number of child nodes in a tree. St000417The size of the automorphism group of the ordered tree. St000422The energy of a graph, if it is integral. St000455The second largest eigenvalue of a graph if it is integral. St000508Eigenvalues of the random-to-random operator acting on a simple module. St000633The size of the automorphism group of a poset. St000640The rank of the largest boolean interval in a poset. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000679The pruning number of an ordered tree. St000741The Colin de Verdière graph invariant. St000753The Grundy value for the game of Kayles on a binary word. St000850The number of 1/2-balanced pairs in a poset. St000907The number of maximal antichains of minimal length in a poset. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001058The breadth of the ordered tree. St001301The first Betti number of the order complex associated with the poset. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001371The length of the longest Yamanouchi prefix of a binary word. St001399The distinguishing number of a poset. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St001462The number of factors of a standard tableaux under concatenation. St001488The number of corners of a skew partition. St001524The degree of symmetry of a binary word. St001534The alternating sum of the coefficients of the Poincare polynomial of the poset cone. St001569The maximal modular displacement of a permutation. St001631The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St001699The major index of a standard tableau minus the weighted size of its shape. St001713The difference of the first and last value in the first row of the Gelfand-Tsetlin pattern. St001730The number of times the path corresponding to a binary word crosses the base line. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001964The interval resolution global dimension of a poset. St000166The depth minus 1 of an ordered tree. St000173The segment statistic of a semistandard tableau. St000174The flush statistic of a semistandard tableau. St000522The number of 1-protected nodes of a rooted tree. St000527The width of the poset. St000682The Grundy value of Welter's game on a binary word. St000691The number of changes of a binary word. St000717The number of ordinal summands of a poset. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000983The length of the longest alternating subword. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St001754The number of tolerances of a finite lattice. St000094The depth of an ordered tree. St000116The major index of a semistandard tableau obtained by standardizing. St000189The number of elements in the poset. St000327The number of cover relations in a poset. St000413The number of ordered trees with the same underlying unordered tree. St000521The number of distinct subtrees of an ordered tree. St000635The number of strictly order preserving maps of a poset into itself. St000847The number of standard Young tableaux whose descent set is the binary word. St000909The number of maximal chains of maximal size in a poset. St000973The length of the boundary of an ordered tree. St000975The length of the boundary minus the length of the trunk of an ordered tree. St001313The number of Dyck paths above the lattice path given by a binary word. St001645The pebbling number of a connected graph. St001879The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St000680The Grundy value for Hackendot on posets. St001268The size of the largest ordinal summand in the poset. St001343The dimension of the reduced incidence algebra of a poset. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001472The permanent of the Coxeter matrix of the poset. St000017The number of inversions of a standard tableau. St000104The number of facets in the order polytope of this poset. St000151The number of facets in the chain polytope of the poset. St000348The non-inversion sum of a binary word. St000526The number of posets with combinatorially isomorphic order polytopes. St000912The number of maximal antichains in a poset. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001397Number of pairs of incomparable elements in a finite poset. St001695The natural comajor index of a standard Young tableau. St001698The comajor index of a standard tableau minus the weighted size of its shape. St001718The number of non-empty open intervals in a poset. St000656The number of cuts of a poset. St001398Number of subsets of size 3 of elements in a poset that form a "v". St001533The largest coefficient of the Poincare polynomial of the poset cone. St001717The largest size of an interval in a poset. St001721The degree of a binary word. St000415The size of the automorphism group of the rooted tree underlying the ordered tree. St000543The size of the conjugacy class of a binary word. St000626The minimal period of a binary word. St000524The number of posets with the same order polynomial. St000180The number of chains of a poset. St000400The path length of an ordered tree. St001779The order of promotion on the set of linear extensions of a poset. St000391The sum of the positions of the ones in a binary word. St001909The number of interval-closed sets of a poset. St000070The number of antichains in a poset. St000016The number of attacking pairs of a standard tableau. St000479The Ramsey number of a graph. St000641The number of non-empty boolean intervals in a poset. St000529The number of permutations whose descent word is the given binary word. St000639The number of relations in a poset. St001838The number of nonempty primitive factors of a binary word. St000416The number of inequivalent increasing trees of an ordered tree. St000950Number of tilting modules of the corresponding LNakayama algebra, where a tilting module is a generalised tilting module of projective dimension 1. St000631The number of distinct palindromic decompositions of a binary word. St000294The number of distinct factors of a binary word. St000525The number of posets with the same zeta polynomial. St000634The number of endomorphisms of a poset. St001664The number of non-isomorphic subposets of a poset. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St000347The inversion sum of a binary word. St000518The number of distinct subsequences in a binary word. St000949Gives the number of generalised tilting modules of the corresponding LNakayama algebra. St001885The number of binary words with the same proper border set. St001709The number of homomorphisms to the three element chain of a poset. St000410The tree factorial of an ordered tree. St000826The stopping time of the decimal representation of the binary word for the 3x+1 problem. St001560The product of the cardinalities of the lower order ideal and upper order ideal generated by a permutation in weak order. St000289The decimal representation of a binary word. St001815The number of order preserving surjections from a poset to a total order. St000827The decimal representation of a binary word with a leading 1. St001243The sum of coefficients in the Schur basis of certain LLT polynomials associated with a Dyck path. St001813The product of the sizes of the principal order filters in a poset. St001916The number of transient elements in the orbit of Bulgarian solitaire corresponding to a necklace. St001915The size of the component corresponding to a necklace in Bulgarian solitaire. St001242The toal dimension of certain Sn modules determined by LLT polynomials associated with a Dyck path. St001408The number of maximal entries in a semistandard tableau.